A305252 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 3, 5, 3, 5, 7, 7, 5, 8, 17, 10, 17, 8, 13, 35, 17, 17, 35, 13, 21, 61, 34, 42, 34, 61, 21, 34, 127, 65, 79, 79, 65, 127, 34, 55, 265, 121, 163, 203, 163, 121, 265, 55, 89, 507, 244, 356, 439, 439, 356, 244, 507, 89, 144, 1013, 502, 794, 1010, 1149, 1010, 794, 502, 1013

Offset

1,2

Comments

Table starts

..1...2...3....5....8....13....21.....34......55......89......144.......233

..2...5...7...17...35....61...127....265.....507....1013.....2071......4097

..3...7..10...17...34....65...121....244.....502....1023.....2112......4430

..5..17..17...42...79...163...356....794....1699....3824.....8679.....19781

..8..35..34...79..203...439..1010...2382....5699...13811....33747.....82601

.13..61..65..163..439..1149..2985...8254...22801...62473...173206....483696

.21.127.121..356.1010..2985..9288..29714...94491..302488...974340...3152830

.34.265.244..794.2382..8254.29714.110121..399364.1469285..5435109..20207222

.55.507.502.1699.5699.22801.94491.399364.1688401.7171215.30542434.130768430

Links

R. H. Hardin, Table of n, a(n) for n = 1..312

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) -4*a(n-4) for n>5

k=3: [order 12]

k=4: [order 26] for n>30

k=5: [order 54] for n>59

Example

Some solutions for n=5 k=4
..0..0..0..0. .0..1..1..1. .0..0..0..0. .0..1..1..1. .0..1..1..1
..0..0..0..0. .1..1..1..1. .0..0..1..0. .0..0..1..1. .1..1..1..1
..0..0..0..0. .1..1..1..1. .0..0..0..0. .0..0..0..1. .1..1..1..1
..0..0..1..0. .1..1..1..1. .0..0..0..0. .0..0..0..0. .1..1..1..1
..0..0..0..0. .0..1..1..0. .1..0..0..0. .0..0..0..0. .0..1..1..1

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A303802.

Sequence in context: A306129 A304221 A305482 * A316552 A316311 A317266

Adjacent sequences: A305249 A305250 A305251 * A305253 A305254 A305255

Keyword

nonn,tabl

Author

R. H. Hardin, May 28 2018

Status

approved